Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON3):

Solution:
from math import sqrt

def find(k, n):
    l = 1
    r = n
    while l <= r:
        m = l + (r - l) // 2
        a = k ** 2
        b = m ** 2
        if a + b + m + k == 2 * n:
            return True
        elif a + b + m + k < 2 * n:
            l = m + 1
        else:
            r = m - 1
    return False


def main():
    for _ in range(1):
        n = int(input())
        flag = False

        for k in range(1, int(sqrt(10 ** 9)) + 1):
            if find(k, n):
                flag = True
                break

        print("YES" if flag else "NO")

if __name__ == "__main__":
    main()